IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v592y2022ics0378437121009912.html
   My bibliography  Save this article

Size distribution of states, counties, and cities in the USA: New inequality form information

Author

Listed:
  • Grachev, Gennady A.

Abstract

In this article, we propose a new approach for studying the patterns of size distribution in settlement systems, based on the analysis of the shape of the Pareto curve (PC). To study the shape of the PC, we used the Gini coefficient, the asymmetry coefficient, and, by analogy with the physics of phase transitions, critical exponent — the index of the PC degree in the neighborhood of zero. An empirical analysis of the PC of various levels of aggregation in the US settlement system has been performed. The form of size distribution of states was studied by decades from 1790 to 2010. The spatial analysis of the PC shape for counties and cities was performed for 2010. The results of an empirical study showed that the PC of the states had left-hand asymmetry over 220 years. The PC of counties and cities had both right-hand and left-hand asymmetries. The obtained results explain in which cases the Pareto distribution having a PC with right-hand asymmetry, and the lognormal distribution with a symmetric PC may not correspond objectively to real settlement systems. As an alternative to power-series distribution and lognormal distribution, we considered an analytically simple two-parameter model with a wide range of PC asymmetry that combines the properties of power-series distribution and lognormal distribution. Verification of the model showed that it adequately described the size of settlements in homogeneous settlement systems.

Suggested Citation

  • Grachev, Gennady A., 2022. "Size distribution of states, counties, and cities in the USA: New inequality form information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    • Handle: RePEc:eee:phsmap:v:592:y:2022:i:c:s0378437121009912
    DOI: 10.1016/j.physa.2021.126831
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121009912
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126831?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    2. Ghosh, Abhik & Basu, Banasri, 2019. "Universal City-size distributions through rank ordering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    3. Benguigui, Lucien & Blumenfeld-Lieberthal, Efrat, 2007. "A dynamic model for city size distribution beyond Zipf's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 613-627.
    4. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2018. "Zipf’s law and city size distribution: A survey of the literature and future research agenda," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 75-92.
    5. Banerjee, Suchismita & Chakrabarti, Bikas K. & Mitra, Manipushpak & Mutuswami, Suresh, 2020. "On the Kolkata index as a measure of income inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    6. Fabio Clementi & Mauro Gallegati & Lisa Gianmoena & Simone Landini & Joseph E. Stiglitz, 2019. "Mis-measurement of inequality: a critical reflection and new insights," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(4), pages 891-921, December.
    7. Kwok Tong Soo, 2012. "The size and growth of state populations in the United States," Economics Bulletin, AccessEcon, vol. 32(2), pages 1238-1249.
    8. Ekrem Aydiner & Andrey G. Cherstvy & Ralf Metzler, 2019. "Money distribution in agent-based models with position-exchange dynamics: the Pareto paradigm revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(5), pages 1-4, May.
    9. Rasche, R H, et al, 1980. "Functional Forms for Estimating the Lorenz Curve: Comment," Econometrica, Econometric Society, vol. 48(4), pages 1061-1062, May.
    10. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.
    11. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2013. "The size distribution of US cities: Not Pareto, even in the tail," Economics Letters, Elsevier, vol. 120(2), pages 232-237.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hasan Engin Duran & Andrzej Cieślik, 2021. "The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(5), pages 1702-1719, October.
    2. Angelina Hackmann & Torben Klarl, 2020. "The evolution of Zipf's Law for U.S. cities," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 841-852, June.
    3. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    4. Pengfei Li & Ming Lu, 2021. "Urban Systems: Understanding and Predicting the Spatial Distribution of China's Population," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 29(4), pages 35-62, July.
    5. SHIDA, Yoshisada, 2021. "Does the Currency Crisis Veil the Impact of Economic Sanctions under an Authoritarian Regime? An Inquiry into Russia," RRC Working Paper Series 91, Russian Research Center, Institute of Economic Research, Hitotsubashi University.
    6. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    7. Huan Li & Yehua Dennis Wei & Yuemin Ning, 2016. "Spatial and Temporal Evolution of Urban Systems in China during Rapid Urbanization," Sustainability, MDPI, vol. 8(7), pages 1-17, July.
    8. Ruz, Soumendra Nath, 2023. "Amazing aspects of inequality indices (Gini and Kolkata Index) of COVID-19 confirmed cases in India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P2).
    9. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    10. Miguel Puente-Ajovín & Marcos Sanso-Navarro & María Vera-Cabello, 2022. "The distribution of urban population and economic activity in the European Union and the United States," Letters in Spatial and Resource Sciences, Springer, vol. 15(3), pages 517-522, December.
    11. Kazuhiro Kumo & Elena Shadrina, 2021. "On the Evolution of Hierarchical Urban Systems in Soviet Russia, 1897–1989," Sustainability, MDPI, vol. 13(20), pages 1-17, October.
    12. Cieślik Andrzej & Teresiński Jan, 2016. "Does Zipf’s law hold for Polish cities?," Miscellanea Geographica. Regional Studies on Development, Sciendo, vol. 20(4), pages 5-10, December.
    13. Piotr Gabrielczak & Tomasz Serwach, 2019. "Firm-size distribution in Poland – is power law applicable?," Lodz Economics Working Papers 3/2019, University of Lodz, Faculty of Economics and Sociology.
    14. Asif, Muhammad & Hussain, Zawar & Asghar, Zahid & Hussain, Muhammad Irfan & Raftab, Mariya & Shah, Said Farooq & Khan, Akbar Ali, 2021. "A statistical evidence of power law distribution in the upper tail of world billionaires’ data 2010–20," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    15. Josic Hrvoje & Bašić Maja, 2018. "Reconsidering Zipf’s law for regional development: The case of settlements and cities in Croatia," Miscellanea Geographica. Regional Studies on Development, Sciendo, vol. 22(1), pages 22-30, March.
    16. Rafael González-Val, 2019. "US city-size distribution and space," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 283-300, July.
    17. Rafael González-Val, 2011. "Deviations from Zipf’s Law for American Cities," Urban Studies, Urban Studies Journal Limited, vol. 48(5), pages 1017-1035, April.
    18. Montebruno, Piero & Bennett, Robert J. & van Lieshout, Carry & Smith, Harry, 2019. "A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 858-875.
    19. Inho Hong & Woo-Sung Jung & Hang-Hyun Jo, 2019. "Gravity model explained by the radiation model on a population landscape," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-13, June.
    20. Pankaj Bajracharya & Selima Sultana, 2020. "Rank-size Distribution of Cities and Municipalities in Bangladesh," Sustainability, MDPI, vol. 12(11), pages 1-26, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:592:y:2022:i:c:s0378437121009912. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.